A quadrature method is derived for calculating the incompressible-flow aerodynamics of arbitrarily cambered jet-flapped airfoils. The anticipated application of the methodology is to high-speed subsonic flows (combat maneuvering aircraft) via the use of compressible-flow similarity transformations. The method yields the aerodynamic properties in terms of integrals having integrands which consist of the product of the camber-line ordinate and an influence function which is a parametric function of the jet-momentum coefficient. In general, the integrals involved must be evaluated by numerical methods. Tables of the necessary influence functions are given in the report.